Roulette,
a solved game.
Roulette is the cleanest negative-expectation game on the floor. Every bet has the same expected value per dollar wagered. No system, betting pattern, or progression changes that. The only meaningful decision is which wheel and which rule set you sit at.
One choice that doubles your house edge
The single most important roulette decision happens before the first bet: pick the European (single-zero) or French (single-zero with rule) wheel, not the American (double-zero) wheel. The math difference is:
European wheel 37 pockets: 1 to 36 plus single 0 even-money win probability = 18/37 = 48.65% EV per $1 = (18/37 × $1) − (19/37 × $1) = −$0.027 → 2.70% house edge American wheel 38 pockets: 1 to 36 plus 0 and 00 even-money win probability = 18/38 = 47.37% EV per $1 = (18/38 × $1) − (20/38 × $1) = −$0.0526 → 5.26% house edge Same game. Same bets. Almost double the cost on American.
Crypto casinos generally default to European or French wheels. American shows up on a handful of US-facing operators and some older RNG variants. If a roulette lobby gives you a choice, the single-zero option is the only correct answer.
House edge is constant, mostly
Every standard roulette bet on a single-zero wheel has the same 2.70% house edge. The bets differ in volatility, not expected value. The exception is the basket bet (5-number top line, only on American wheels), which is worse.
| Bet | Pays | Win prob (single zero) | House edge |
|---|---|---|---|
| Straight (single number) | 35:1 | 1/37 = 2.70% | 2.70% |
| Split (two numbers) | 17:1 | 2/37 = 5.41% | 2.70% |
| Street (three) | 11:1 | 3/37 = 8.11% | 2.70% |
| Corner (four) | 8:1 | 4/37 = 10.81% | 2.70% |
| Six line (six) | 5:1 | 6/37 = 16.22% | 2.70% |
| Column / dozen | 2:1 | 12/37 = 32.43% | 2.70% |
| Even-money (red/black, even/odd, hi/lo) | 1:1 | 18/37 = 48.65% | 2.70% |
| Even-money WITH La Partage | 1:1 (lose half on 0) | 48.65% | 1.35% |
| Basket (5-number, American only) | 6:1 | 5/38 = 13.16% | 7.89% |
The takeaway is liberating: bet whatever pattern you find fun. The math doesn’t care. Inside bets give you bigger swings; outside bets give you smaller swings. The cost per dollar wagered is identical, except for the basket bet (skip) and even-money on a French wheel (the best deal in the room).
La Partage and En Prison
French wheels (and some European tables that opt in) offer two rules that halve the house edge on even-money bets:
- La Partage: when zero hits, even-money bets lose half instead of all. Your $10 red bet loses $5 on zero, not $10.
- En Prison: when zero hits, the bet is imprisoned for one more spin. If it wins next, you get it back at no profit. EV identical to La Partage.
La Partage on red, $10 bet win : +$10 (probability 18/37) lose (non-zero black): -$10 (probability 18/37) zero : -$5 (probability 1/37) EV = (18/37 × $10) + (18/37 × −$10) + (1/37 × −$5) = (180 − 180 − 5) / 37 = −5/37 = −$0.135 per $10 wagered → 1.35% house edge
If a crypto-casino live roulette table offers French rules, the even-money bets there are the lowest-house-edge non-skill bets you will find anywhere on the floor. 1.35% beats most crypto-casino blackjack tables once game-weighting is factored in.
Every betting system loses
Betting systems (Martingale, Fibonacci, Labouchère, d’Alembert, Paroli) all promise a way around the house edge by sizing differently after wins or losses. They share one feature: none of them work, because none of them change EV per dollar wagered. They redistribute outcomes; they do not move the average.
| System | Idea | Why it fails |
|---|---|---|
| Martingale | Double bet after every loss until you win | Geometric escalation. A 7-loss streak (probability ~0.6%) needs $1280 from a $10 base; table limits or bankroll cut you off before recovery. |
| Fibonacci | Bet next Fibonacci number after a loss; back two on a win | Smoother escalation, same end-state. Eventually the streak you cannot afford arrives, and the cumulative loss is real. |
| Labouchère | Cancel numbers from a list as you win/lose | Adds bookkeeping. Same EV. Long sequences require huge stakes near the end. |
| d'Alembert | Increase by 1 unit after loss, decrease by 1 after win | Linear progression, smaller blowups. Still negative-EV; small wins exactly cancel small losses, and any persistent down-stretch leaves a real loss. |
| Paroli | Triple bet after a win, reset after loss | Reverse-Martingale on wins. Doesn't change EV. It is just bigger wins followed by a giveback. |
The proof is short. EV is linear: EV(bet1) + EV(bet2) + ... + EV(betN) = N × EV(single bet). If each bet has the same negative EV, the sum is negative regardless of how you ordered the sizes. Sizing patterns rearrange the shape of the loss distribution, never the mean.
Live dealer vs RNG roulette
The math is identical when the rule sets match. Differences are operational:
- RNG roulette: spin every 5 to 15 seconds. Higher hands-per-hour means higher exposure to the house edge over a session. Solo experience.
- Live dealer: spin every 35 to 60 seconds. Slower pace lowers your dollar-per-hour loss rate at the same bet size. Studio production, multi- player, French rules more common.
- Lightning Roulette and similar: Evolution’s gimmick variant. Random number multipliers (50× to 500×) are paid for by reduced straight-up payout (29:1 instead of 35:1). House edge climbs to ~2.94%. Marketed as “bigger wins.”
For pure EV, French live roulette with La Partage is the lowest-edge option. For pure variance, RNG straight-up bets at higher tempo. Almost everything else is in between.
